Castelnuovo theory and the geometric Schottky problem

Details Castelnuovo theory and the geometric Schottky problem Castelnuovo theory and the geometric Schottky problem

2004-07-22

arxiv.org/abs/math/0407370v4

Mathematics

Algebraic Geometry

17 pages; final version, to appear in J. Reine Angew. Math.; no significant changes, only some small corrections and additions

Scientific paper

We prove and conjecture results which show that Castelnuovo theory in projective space has a close analogue for abelian varieties. This is related to the geometric Schottky problem: our main result is that a principally polarized abelian variety satisfies a precise version of the Castelnuovo Lemma if and only if it is a Jacobian. This result has a surprising connection to the Trisecant Conjecture. We also give a genus bound for curves in abelian varieties.

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